How to bake object with cloth simulation and subsurf (not applied)? Having trouble using .mdd method
Enable the .mdd file importer / exporter addon:

Select an object with the cloth simulation and subsurf (not applied). CTRL + A - apply rotation, scale and location. Note that if some other objects, which are parented (or vertex parented) to that object, after applying operation, they may change their position and rotation. To avoid it, unparent them (ALT + P - Clear Parent), before applying, then apply rotation, scale and position, and then parent them back.
While the object with ththe cloth simulation is selected, export the .mdd file. Export may take some time.
After  export - remove the Cloth simulation.
Unparent (ALT + P - Clear Parent).
Apply subsurf.
At this stage, I usially re-applying rotation, scale and position, just in case - (CTRL + A).
While the object is still selected - import .mdd file.


Play the animation, or select a different current frame to update the final result. Note that the shape key animation rather increases the size of the project.



Many thanks to  Mr Zak, m.ardito from blender.stackexchange.com and to Richard Marklew, benu from blenderartists.org for their help in finding solution!